Michel Bataille, Cyclic quadrilaterals with prescribed Varignon
Forum Geometricorum, 7 (2007) 199--206.
Abstract: We prove that the vertices of a given parallelogram P are the midpoints
of the sides of infinitely many cyclic quadrilaterals and show how to construct
such quadrilaterals. Then we discuss some of their properties and identify
related loci. Lastly, the cases when P is a rectangle or a rhombus are examined.